Method and arrangement for adapting a multi-antenna transmission

ABSTRACT

A method in a first node for adapting a multi-antenna transmission to a second node over a wireless channel is provided. The wireless channel has at least three inputs and at least one output. The first node and the second node are comprised in a wireless communication system. The method comprising the steps of: Obtaining ( 401 ) at least one symbol stream; Determining ( 403 ) a precoding matrix having a product structure created by a block diagonal matrix being multiplied from the left with a block diagonalizing unitary matrix; Precoding ( 404 ) the at least one symbol stream with the determined precoding matrix; And Transmitting ( 405 ) the precoded at least one symbol stream over a wireless channel to the second node.

TECHNICAL FIELD

The present invention relates to a method and an arrangement in a firstnode and a method and an arrangement in a second node. In particular, itrelates to adaptation of a multi-antenna transmission from the firstnode to the second node over a wireless channel.

BACKGROUND

The use of multiple antennas at a transmitter and/or a receiver of anode in a wireless communication system may significantly boost thecapacity and coverage of the wireless communication system. SuchMultiple Input Multiple Output (MIMO) systems exploit the spatialdimension of the communication channel to improve performance by forexample transmitting several parallel information carrying signals,so-called spatial multiplexing. By adapting the transmission to thecurrent channel conditions, significant additional gains may beachieved. One form of adaptation is to dynamically, from oneTransmission Time Interval (TTI) to another, adjust the number ofsimultaneously transmitted information carrying signals to what thechannel may support. This is commonly referred to as transmission rankadaptation. Precoding is another related form of adaptation where thephases and amplitudes of the aforementioned signals are adjusted tobetter fit the current channel properties. Classical beam-forming is aspecial case of precoding in which the phase of an information-carryingsignal is adjusted on each transmit antenna so that all the transmittedsignals add constructively at the receiver.

The signals form a vector-valued signal and the adjustment may bethought of as multiplication by a precoder matrix. The precoder matrixis chosen based on information about the channel properties. A commonapproach is to select the precoder matrix from a finite and countableset, a so-called codebook. Such codebook based precoding is an integralpart of the Long Term Evolution (LTE) standard and will be supported inMIMO for High Speed Downlink Packet Access (HSDPA) in Wideband CodeDivision Multiple Access (WCDMA) as well. The receiver (e.g. UserEquipment, UE) would then typically evaluate all the different precodermatrices in the codebook and signal to the transmitter (e.g. Node B)which element is preferred. The transmitter would then use the signalledinformation, when deciding which precoder matrix to apply. Sincecodebook indices need to be signalled and the receiver needs to select asuitable codebook element, it is important to keep the codebook size assmall as possible. On the other hand, larger codebooks ensure that it ispossible to find an entry that matches the current channel conditionsmore closely.

Codebook based precoding may be seen as a form of channel quantization.Alternatively, methods may be used that compute the precoder matrixwithout resorting to quantization.

The fundamental goal of precoder codebook design is to keep the codebooksize small while still achieving as high performance as possible. Designof the elements in the codebook thus becomes crucial in order to achievethe intended performance.

Different antenna array configurations influence how the codebookelements should be designed. Many existing solutions are designed withspatially uncorrelated channel fading in mind and where each channelcoefficient fades with the same average power. However, such a channelmodel is not sufficiently accurate when cross-polarized antenna arraysare used. Consequently, the existing designs are ill-suited for such aconfiguration—an antenna configuration which is deemed important inpractice.

To understand why existing designs tailored for equal powered channelcoefficients are not efficient for a cross-polarized antenna arraysetup, consider for simplicity a 2×2 MIMO system in which both thetransmitter and the receiver use cross-polarized arrays and the twoorthogonal polarizations are aligned on the transmit and receive side,e.g. a pair of vertically and horizontally polarized antennas on bothsides of the link. The MIMO channel matrix will then be diagonallyheavy, meaning that the on-diagonal elements on average havesubstantially more power than the off-diagonal ones, since the verticaland horizontal polarizations are on average fairly well-separated evenafter experiencing the radio channel and reaching the receiver. For sucha channel, an appropriate codebook of minimal size contains the unitvectors and the identity matrix. This ensures that when one-streamtransmission (rank-one transmission) is performed, all the transmitpower may be allocated to the antenna with the strong channel and nopower is wasted on the other antenna, which on average will not be ableto convey significant power to the receiver. The reason for the latteris because of the cross-polarized setup in conjunction with theselection of rank-one transmission, which means the channel matrix willtypically have only one element with a power substantially larger thanzero and that element will lie on the diagonal.

All power should hence be allocated to the antenna which corresponds tothe aforementioned non-zero diagonal element. For a precoder designwhich targets a scenario with equal powered channel coefficients, thisis however typically not the case. This is ensured by a diagonalprecoder structure or precoder codebook structure. For MIMO systems withmore than two transmission (Tx) antennas, a block diagonal structure issuitable.

As already mentioned, cross-polarized arrays with vertical andhorizontal polarization at transmitter tend to result in well-separatedtransmission pipes, which is attractive for multi-stream MIMOtransmission. The common use of +−45 degree cross-polarized arrays arefrom this perspective not as attractive since the transmissions from thetwo different polarization mix on both the vertical as well as on thehorizontal polarization. This potentially increases inter-streaminterference and therefore hurts MIMO performance. A block diagonalprecoder structure is thus not optimized for the +−45 cross-polarizedcase, which is a very common setup in existing deployments.

Another problem with a block diagonal structure is that it leads topower imbalance problems among the Power Amplifiers (PA)s. All PAs arenot running on full power unless pooling of PAs is used so that poweramong the PAs can be shared. Pooling PAs can however be complicated andexpensive and is sometimes even not possible.

In practice the degree of separation between horizontal and verticalpolarization may vary and thus increase inter-stream interference if theMIMO scheme solely relies on polararization to separate the streams.This also means that a purely block diagonal precoder may not bedesirable. A mix of block diagonal elements and other elements may infact be appropriate. This generally leads to a power imbalance problemon amplifiers, and because of the mix of block diagonal and non blockdiagonal elements, existing techniques for pooling PAs are no longeruseful.

SUMMARY

The objective problem is to provide a mechanism for improving theperformance of a wireless channel when using precoding.

According to a first aspect of the present invention, the object isachieved by a method in a first node for adapting a multi-antennatransmission to a second node over a wireless channel. The wirelesschannel has at least three inputs and at least one output. The firstnode and the second node are comprised in a wireless communicationsystem. The method comprises the steps of obtaining at least one symbolstream, and determining a precoding matrix having a product structurecreated by a block diagonal matrix being multiplied from the left with ablock diagonalizing unitary matrix. The method comprises the furthersteps of precoding the at least one symbol stream with the determinedprecoding matrix, and transmitting the precoded at least one symbolstream over a wireless channel to the second node.

According to a second aspect of the present invention, the object isachieved by a method in a second node for receiving a multi-antennatransmission from a first node over a wireless channel. The wirelesschannel has at least three inputs and at least one output. The firstnode and the second node are comprised in a wireless communicationsystem. The method comprises the step of receiving a transmissioncorresponding to at least one symbol stream over a wireless channelconveyed from the first node. The at least one symbol stream is precodedwith a precoding matrix having a product structure created by a blockdiagonal matrix being multiplied from the left with a blockdiagonalizing unitary matrix.

According to a third aspect of the present invention, the object isachieved by an arrangement in a first node for adapting a multi-antennatransmission to a second node over a wireless channel. The wirelesschannel has at least three inputs and at least one output. The firstnode and the second node are comprised in a wireless communicationsystem. The first node arrangement comprises an obtaining unitconfigured to obtain at least one symbol stream, and a determining unitconfigured to determine a precoding matrix having a product structurecreated by a block diagonal matrix being multiplied from the left with ablock diagonalizing unitary matrix. The first node arrangement furthercomprises precoding unit configured to precode the at least one symbolstream with the determined precoding matrix, and a transmitting unitconfigured to transmit the precoded at least one symbol stream over awireless channel to the second node.

According to a fourth aspect of the present invention, the object isachieved by an arrangement in a second node for receiving amulti-antenna transmission from a first node over a wireless channel.The wireless channel having at least three inputs and at least oneoutput. The first node and the second node are comprised in a wirelesscommunication system. The second node arrangement comprises a receivingunit configured to receive a transmission corresponding to at least onesymbol stream over a wireless channel conveyed from the first node. Theat least one symbol stream is precoded with a precoding matrix having aproduct structure created by a block diagonal matrix being multipliedfrom the left with a block diagonalizing unitary matrix.

A precoding matrix having a product structure is used. The precodingmatrix having a product structure is created by a block diagonal matrixbeing multiplied with a block diagonalizing unitary matrix. Using thismatrix having a product structure for precoding a symbol stream whentransmitting it over a wireless link, helps balancing the PAs. Thisimplies that more power can be emitted into the propagation channelresulting in an improved performance of the wireless channel.

It is evidenced by the fact that a codebook multiplied by the mentionedunitary matrices produce a new codebook where each element in eachmatrix/vector has the same magnitude. Of particular interest is the useof a so-called block diagonalizing unitary matrix together with thecommonly deployed +−45 polarized antennas, which simultaneously achievespower balancing and desirable rotation to polarized transmission in thehorizontal and vertical direction even in the case of a mixture of blockdiagonal and some non-block diagonal precoder elements.

An advantage with the present solution is that using the matrix having aproduct structure, improves performance by e.g. allowing higher datarates or better reliability, particularly when the polarizations are notperfectly separated (e.g. moderate cross polar discrimination (XPD))when used in conjunction with +−45 degree polarized arrays. The use ofthe PAs is also optimized thus reducing the power consumption as well asheat dissipation.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in more detail with reference to attacheddrawings illustrating exemplary embodiments of the invention and inwhich:

FIG. 1 is a schematic block diagram illustrating embodiments of awireless communication system.

FIG. 2 is a schematic block diagram illustrating embodiments of awireless communication system.

FIG. 3 is a schematic block diagram illustrating embodiments of a firstnode.

FIG. 4 is a flow chart illustrating embodiments of a method in a firstnode.

FIG. 5 is a schematic block diagram illustrating embodiments of a firstnode arrangement.

FIG. 6 is a flow chart illustrating embodiments of a method in a secondnode.

FIG. 7 is a schematic block diagram illustrating embodiments of a secondnode arrangement.

DETAILED DESCRIPTION

The invention is defined as a method and an arrangement in a respectivefirst and second node, which may be put into practice in the embodimentsdescribed below.

FIG. 1 depicts a first node 100 in a wireless communication system 110.The wireless communication system 110 may be a cellular system and/or asystem such as e.g. Long Term Evolution (LTE), Evolved—UniversalTerrestrial Radio Access (E-UTRA), Worldwide Interoperability forMicrowave Access (WiMAX), Universal Terrestrial Radio Access (UTRA),Wideband Code Division Multiple Access (WCDMA), GSM, Ultra MobileWideband (UMB) or any other wireless communication system usingtechnologies that perform adaptation between different forms oftransmission and use multiple antennas. The first node 100 is arrangedto communicate with a second node 120 in the wireless communicationsystem 110 over a wireless channel 130. A linear and time-invariant MIMOfilter may be used to model the input-output relation of the wirelesschannel during a sufficiently short transmission period. Forsufficiently narrowband transmissions, a single matrix may be used fordescribing the filter. Such a channel matrix description also holds formodelling the channel over a subcarrier, (or several subcarriers as longthey span a bandwidth which is small compared with the coherencebandwidth of the channel) in an Orthogonal Frequency DivisionMultiplexing (OFDM) system such as e.g. LTE. The first node 100 may beany type of a base station such as e.g. a NodeB as in LTE. The secondnode 120 may be a user equipment (UE) such as e.g. a mobile phone, aPersonal Digital Assistant (PDA), a laptop. It may also be the other wayaround, that the first node 100 may be a UE such as e.g. a mobile phone,a Personal Digital Assistant (PDA) and the second node 120 may be anytype of a base station such as e.g. a NodeB. In the example of FIG. 1,the first node 100 is a base station and the second node 120 is a userequipment. In addition, the first node 100 and the second node 120 mayconstitute arbitrary wireless devices in communication with each otherand with no particular hierarchical ordering.

The first node 100 uses a multiple antenna system, i.e. uses multipleantennas for its transmission to the second node 120. The second node120 may also use a multiple antenna system for reception of the firstnode's transmission. This is thus a MIMO system, where the inputs to thechannel corresponds to the transmit antennas in the first node 100 andthe outputs to the receive antennas in the second node 120. Transmitterand receiver filtering/processing may also be considered to be includedinto the channel. Note that such a MIMO setup may include the specialcase of only one receive antenna. FIG. 2 illustrates some embodimentswherein the first node 100 and a second node 120 are each using amultiple antenna system comprising four antennas. The first node 100obtains an information carrying signal 140 being represented by asequence of information bits, which information is to be conveyed to thesecond node 120 over the wireless channel 130. FIG. 2 schematicallyillustrates the first node 100 as being the transmitting node (Tx) andthe second node 120 as being the receiving node (Rx), the first node 100and the second node 120 may use a multiple-antenna system 150, resultingin a MIMO link. In this example the first node 100 comprises fourtransmit antennas 160 1, 2, 3 and 4, e.g. a base station with fourtransmit antennas, and the second node 120 comprises four receiveantennas 170 1, 2, 3 and 4, e.g. a user equipment with four receiveantennas.

In the example of FIG. 2, the first node 100 comprises an encoding unit162, a post precoding unit 163 and four radio transmitter units 164. Theencoding unit 162 is arranged to receive the information carrying signal140 to be transmitted. The encoding unit 162 may further be arranged topossibly demultiplex the information bits into one or severalinformation bit sequences, code these information bit sequences usingsome channel code (e.g. turbo code, low-density parity-check (LDPC)code, convolutional code), modulate the coded bits to produce symbols,map the symbols to a sequence of information carrying symbol vectors andprecode the information carrying symbol vectors and finally forward theresult to a possible post precoding unit 163. The post-precoding unit163 may in the simplest of cases just forward the precoded signal (i.e.,the post precoding unit 163 is transparent and would hence be viewed asnot existing) or it might process it in some way, e.g. perform digitalfiltering in baseband, before outputting possibly processed signals fortransmission utilizing the radio transmitter units 164, using therespective transmit antennas 160 1, 2, 3 and 4 for transmitting theprecoded signal to the second node 120. It is appreciated that the basicfunctions of the transmitter are well known for a skilled person and notdescribed in detail. The transmitter in this example may supporttechniques such as Spatial-Division Multiple Access (SDMA), SDMAprecoding, MIMO, MIMO precoding, and/or MIMO-SDMA.

In the example of FIG. 2, the second node 120 comprises a pre-processingunit 171, a decoding demodulation unit 172 and four radio receiver units174. The second node 120 is arranged to receive the precoded signal fromthe first node 100. The signal is received by means of the receiveantennas 170 1, 2, 3 and 4, the pre-processing unit 171 and the radioreceiver units 174. The pre-processing unit 171 may implement variousprocessing steps, e.g. it may perform filtering in base band or simplyforward the signals unaltered to the decoding demodulation unit 172. Inthe latter case, the pre-processing unit 171 may alternatively beconsidered not to be present (i.e., transparent corresponding to nopre-processing unit). The decoding demodulation unit 172 may be arrangedto receive the coded signal from the pre-processing unit 171. Thedecoding demodulation unit 172 may further be arranged to demodulate thecoded signal to data bits. It is appreciated that the basic functions ofthe receiver are well known for a skilled person and not described indetail herein.

It should also be noticed that both receiver in the second node 120 andtransmitter in the first node 100 may alter operation mode functioningas transmitter and receive, respectively.

Precoding

As already indicated, the encoding unit 162 in the first node 100 can befurther subdivided into two parts, corresponding to a coding andmodulation unit 300 and a precoding unit 310, such as e.g. a precoder.An example of a coding and modulation unit 300 and a precoding unit 310is depicted in FIG. 3. The coding and modulation unit 300 takesinformation bits as input and produces a sequence of informationcarrying symbol vectors, i.e. a vector-valued information-carryingsignal as output. The information carrying symbol vectors can be seen asone or several symbol streams in parallel where each element of eachvector s thus belongs to a certain symbol stream. The different symbolstreams are commonly referred to as layers and at any given moment thereare r different such layers corresponding to a transmission rank of r.Thus, the signal to be transmitted to the second node 120 over thewireless channel 130 comprises at least one symbol stream (or layer).The r symbols in a particular r×1 information carrying symbol vector sis subsequently multiplied by an N_(T)×r precoder matrix W_(N) _(T)_(×r), where N_(T) denotes the number of inputs (e.g. number of transmitantennas, number of antenna ports etc) of the MIMO channel. Thementioned precoding operation forwards the resulting output to thepost-processing unit 163. The first node 100 determines a precodingmatrix having a certain product structure, which will be furtherdescribed in the sequel. This may be performed by choosing a precodingmatrix to match the characteristics of the channel, i.e., to match anN_(R)×N_(T) MIMO channel matrix H. The precoder matrix W_(N) _(T) _(×r)may thus depend on the value of the channel H. The r informationcarrying symbols in s are typically complex-valued. Support of rankadaptation allows the number of simultaneously transmitted symbolstreams, r, to be set to suit the current channel characteristics.Subsequent to precoding, the signals are conveyed over the channel H andreceived by an antenna array with N_(R) elements. The receiver possiblyprocesses the signals by means of the pre-processing unit 171.Collecting the signals into an N_(R)×1 vector y and considering thesignals over a sufficiently narrow bandwidth, compared with thecoherence bandwidth of the channel, gives the modely=HW _(N) _(T) _(×r) s+ewhere e is usually modelled as a noise vector obtained as realizationsof some random process and where the output of the channel thuscorresponds to the output of pre-processing unit 171 (the latter whichmay be transparent). This model obviously also holds for OFDM systems(e.g. LTE, WiMaX etc) where it typically can be applied on a subcarrierbasis.

Channel Matrix, H

Referring again to FIG. 2 the first node 100 comprises a multi-antennasystem where in some embodiments at least one antenna emits radio wavesin a horizontal polarization direction and at least one other antennaemits energy in the orthogonal (i.e., vertical) polarization direction.Such a dual-, or cross-, polarized antenna setup may thus contain agroup of co-polarized antennas and another group of co-polarizedantennas orthogonally polarized relative the former group.“Co-polarization” means the antennas are transmitting with the samepolarization. Under ideal line-of-sight conditions, assuming idealantenna responses and a similar dual-polarized antenna setup at thereceive side, the cross-polarized antenna set-up results in a blockdiagonal channel matrix, which will be further explained below. In theexample of FIG. 2, the first two transmit antennas 160, 1 and 2, arehorizontally polarized and the remaining two, 3 and 4, are verticallypolarized. The receive antennas in the second node 120 are similarlyarranged. The co-polarized antennas in the transmit array may be spacedsufficiently far apart so that the fading is roughly uncorrelated amongthe channels associated with the co-polarized elements. As mentionedabove, the channel may be modelled using a channel matrix. Without lossof generality, by appropriately reordering the transmit and receiveantenna elements, the 4×4 resulting channel matrix H, then tends to havethe block-diagonal structure according to:

$H = \begin{bmatrix}h_{11} & h_{12} & 0 & 0 \\h_{21} & h_{22} & 0 & 0 \\0 & 0 & h_{33} & h_{34} \\0 & 0 & h_{43} & h_{44}\end{bmatrix}$

With such a block-diagonal effective channel matrix, signals transmittedon antennas 160 1 and 2 in the first node 100, do not reach receiveantennas 170 3 and 4, and, correspondingly, signals from transmitantennas 160 3 and 4 do not reach receive antennas 170 1 and 2. Asdepicted in FIG. 2, for the first two transmit antennas 160, 1 and 2being horizontally polarized, the complex-valued channel coefficient h₁₁represents the effective channel involving the physical channel betweentransmit antenna 160 1 and receive antenna 170 1,

the complex-valued channel coefficient h₁₂ represents the effectivechannel involving the physical channel between transmit antenna 160 2and receive antenna 170 1,

the complex-valued channel coefficient h₂₁ represents the effectivechannel involving the physical channel between transmit antenna 160 1and receive antenna 170 2,

the complex-valued channel coefficient h₂₂ represents the effectivechannel involving the physical channel between transmit antenna 160 2and receive antenna 170 2.

Furthermore, as depicted in FIG. 2, for the remaining two transmitantennas 160, 3 and 4 being vertically polarized,

the complex-valued channel coefficient h₃₃ represents the effectivechannel involving the physical channel between transmit antenna 160 3and receive antenna 170 3,

the complex-valued channel coefficient h₃₄ represents the effectivechannel involving the physical channel between transmit antenna 160 4and receive antenna 170 3,

the complex-valued channel coefficient h₄₃ represents the effectivechannel involving the physical channel between transmit antenna 160 3and receive antenna 170 4, and

the complex-valued channel coefficient h₄₄ represents the effectivechannel involving the physical channel between transmit antenna 160 4and receive antenna 170 4.

The general meaning of a block diagonal channel matrix is that it tendsto have the structure

$H = \begin{bmatrix}H_{{\overset{\sim}{M}}_{1} \times {\overset{\sim}{L}}_{1}}^{(1)} & Z_{{\overset{\sim}{M}}_{1} \times {\overset{\sim}{L}}_{2}} & \ldots & Z_{{\overset{\sim}{M}}_{1} \times {\overset{\sim}{L}}_{K}} \\Z_{{\overset{\sim}{M}}_{2} \times {\overset{\sim}{L}}_{1}} & H_{{\overset{\sim}{M}}_{2} \times {\overset{\sim}{L}}_{2}}^{(2)} & \vdots & \vdots \\\vdots & \ldots & \ddots & Z_{{\overset{\sim}{M}}_{K - 1} \times {\overset{\sim}{L}}_{K}} \\Z_{{\overset{\sim}{M}}_{K} \times {\overset{\sim}{L}}_{1}} & \ldots & Z_{{\overset{\sim}{M}}_{K} \times {\overset{\sim}{L}}_{K - 1}} & H_{{\overset{\sim}{M}}_{K} \times {\overset{\sim}{L}}_{K}}^{(K)}\end{bmatrix}$where the matrix can be subdivided into off-diagonal {tilde over(M)}_(k)×{tilde over (L)}_(l), blocks Z_({tilde over (M)}) _(k)_(×{tilde over (L)}) _(l) , k=1, 2, . . . , K≠I=1, 2, . . . , K andon-diagonal {tilde over (M)}_(k)×{tilde over (L)}_(k) blocksH_({tilde over (M)}) _(k) _(×{tilde over (L)}) _(k) ^((k)), k=1, 2, . .. , K of possibly varying sizes. Note that the channel is defined to beblock diagonal if it can be rearranged by means of appropriate row andcolumn permutations to have a form as above such that the average powers(as averaged over sufficiently long time-period so that the fast fadingis averaged out) of the channel coefficients in the off-diagonal blocksZ_({tilde over (M)}) ₁ _(×{tilde over (L)}) ₂ are significantly lowerthan the average powers of the channel coefficients in the on-diagonalblocks H_({tilde over (M)}) _(k) _(×{tilde over (L)}) _(k) ^((k)). Suchsignificantly lower power would e.g. occur if a cross-polarized antennasetup is used in the first node 100 and a similar cross-polarizedantenna setup is used in the second node 120. The difference in averagepower between channel coefficients on the block diagonal and off theblock diagonal is often, depending on the propagation scenario, around 6dB or substantially higher. Even if the antenna setup used in the secondnode 120 is not exactly cross-polarized, the power differences may stillbe significant.

Precoding Matrix Having a Product Structure.

In the present solution, the first node 100 determines a precodingmatrix having a certain product structure. The notion of a productstructure will be presented later and explicitly defined after thediscussion on precoding and codebooks for precoding. The determinedprecoding matrix is to be used for precoding the at least one symbolstream (i.e., one or more layers) to be transmitted to the second node120. The determination may be performed by choosing the precoding matrixto match the characteristics of the channel modelled using the channelmatrix H. If the cross-polarized antenna setup at the first node 100 isusing horizontal and vertically polarized antennas, a precoding withblock diagonal structure is suitable since the use of a block diagonalstructure precoder matches the block diagonal structure of the blockdiagonal channel matrix. However, if the mentioned antenna setup isinstead using polarization oriented for example +−45 degrees, then thechannel matrix is no longer likely to be as block diagonal as ifhorizontal and vertical polarizations would have been used. The precoderproduct structure is in this case beneficial since it involvesdecomposing the precoder into a product of two matrices, one unitary,so-called block diagonalizing unitary matrix, and one block diagonalmatrix, where the latter matrix is multiplied from the left with theformer. The block diagonalizing unitary matrix determined to be used,allows the +−45 degree cross-polarized antenna setup to be transformedinto a virtual 0/90 degree cross-polarized antenna setup (i.e.,horizontally and vertically polarized), which in turn sees a newresulting channel that has a tendency to be block diagonal. Since ablock diagonal virtual channel is effectively obtained, the blockdiagonal precoder in the product structure can now be used to match itscharacteristics. Basically, the unitary matrix serves to rotate thepolarizations so that the transmitted signals align with the verticaland horizontal directions. A benefit of such a product structure is thatthe precoders can be made to have constant modulus elements meaning thatregardless of which exact product structure precoder is used, the samepower is used on all the antenna ports. This thus solves the problem ofhaving to deal with different transmit powers on the different poweramplifiers (PAs). Thus, the product structure not only aligns thetransmission in the beneficial horizontal and vertical polarizations butis also at the same time offering pooling of the PA powers between thesetwo polarizations.

Codebook

Referring to FIG. 2, in some embodiments the first node 100 comprises acodebook 180. The first node 100 may perform the determination of theprecoding matrix having a certain product structure by selecting theprecoding matrix having a product structure from the codebook 180comprised in the first node 100.

In some embodiments the second node 120 comprises a code book 190 asshown in FIG. 2. The second node 120 may select a precoding matrix frome.g. the codebook 190 and recommend the first node to use the selectedprecoding matrix. This may be performed by conveying the recommendedprecoding matrix to the first node 100. The first node 100 may thendecide to use the recommended precoding matrix or exploit the providedchannel information in some other way.

The codebook 180, 190 comprises precoding matrices where each precodingmatrix may correspond to different multiple transmission modes or formsof spatial processing, e.g., channel dependent precoding, MIMOprecoding, SDMA, SDMA with precoding, MIMO-SDMA, etc. Such informationmay be pre-defined. The codebook 180, 190 may further in addition toprecoder matrices/vectors comprise many other parameters such as,transmission ranks, modulation choices, transport block sizes, powersand/or channelization codes etc. In some embodiments the codebook 180,190 comprises a precoder where the transmission rank is implicitly givenby the size of the precoder matrix. The codebook 180, 190 is suitablefor an antenna setup at the first node with not necessarily 0/90 degreepolarizations in that the codebook 180, 190 comprises one or moreprecoding matrices having said product structure. The codebook 180, 190may further comprise precoding matrices having a non-product structure.However, according to the present method, the first node 100 or secondnode 120 is free to select a precoding matrix having said productstructure from the codebook. The codebooks 180 and 190 may be known apriori by both the first node 100 and the second node 120. Also, thetransmitter in the first node 100 may, for example, notify the receiverin the second node 120 of its codebook 180. A suitable codebookstructure will also have a product structure in the meaning that asignificant number of the precoder elements use the product structure.As previously indicated, precoder elements with a product structure maybe written asW=V{tilde over (W)}where V is an N_(T)×N_(T) block diagonalizing unitary matrix and {tildeover (W)} is an N_(T)×r block diagonal matrix.

The block diagonal characteristic of {tilde over (W)} pertains to theplacement of zeros in the precoder matrices. A block diagonal precodermatrix {tilde over (W)}={tilde over (W)}_(N) _(T) _(×r) may in generalbe written as

$\overset{\sim}{W} = \begin{bmatrix}{\overset{\sim}{W}}_{M_{1} \times L_{1}}^{(1)} & 0_{M_{1} \times L_{2}} & \ldots & 0_{M_{1} \times L_{K}} \\0_{M_{2} \times L_{1}} & {\overset{\sim}{W}}_{M_{2} \times L_{2}}^{(2)} & \vdots & \vdots \\\vdots & \ldots & \ddots & 0_{M_{K - 1} \times L_{K}} \\0_{M_{K} \times L_{1}} & \ldots & 0_{M_{K} \times L_{K - 1}} & {\overset{\sim}{W}}_{M_{K} \times L_{K}}^{(K)}\end{bmatrix}$where as seen only the M_(k)×L_(k) blocks {tilde over(W)}_({tilde over (M)}) _(k) _(×{tilde over (L)}) _(k) ^((k)), k=1, 2, .. . , K of possibly varying sizes on the diagonal (in the block domain)may contain non-zero elements. A precoder matrix is considered blockdiagonal if its columns and rows can be permuted so as to achieve theabove form. The rank two case in Table 1 shows an example where theprecoder matrices have the structure

$W = \begin{bmatrix}W_{2 \times 1}^{(1)} & 0_{2 \times 1} \\0_{2 \times 1} & W_{2 \times 1}^{(2)}\end{bmatrix}$Also note that a block may be of size 1×1. Thus, the identity matrix canalso be considered to have a block diagonal structure.

One example of a block diagonalizing unitary matrix is given by

$\left\lbrack \left. \quad\begin{matrix}1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1}\end{matrix} \right\rbrack \right.$which, assuming a N_(T)=4 Tx antenna array where the first two antennashave a +45 polarization direction and the two last have a −45 degreepolarization direction, will rotate the +−45 degree polarizations so asto align with the horizontal and vertical direction. Combined with theblock diagonal elements {tilde over (W)} in the set displayed in Table1, the transmission can be viewed as coming from a block diagonalcodebook applied to an antenna setup with vertically and horizontallypolarized antennas. By multiplying the block diagonalizing unitary Vwith the {tilde over (W)} matrices in Table 1, the codebook of precoderelements in Table 2 is obtained. As seen, all the scalar elements ineach precoder matrix have the same absolute value implying a balanceddesign in that regardless of which precoder element is chosen, thesignals corresponding to the various antenna ports/transmit antennas allhave the same power. Thus, the PAs can be fully utilized from theperspective of the precoding operation.

TABLE 1 Table 1: Example of a set of block diagonal {tilde over (W)}matrices suitable especially well for two spatially separated (smalldistance) cross polarized antenna pairs in SU-MIMO mode. Tx RankCodebook per Rank 1 ${\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\0 \\0\end{bmatrix}},{k = 0},{\ldots\mspace{14mu} 3}$${\frac{1}{\sqrt{2}}\begin{bmatrix}0 \\0 \\1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)}\end{bmatrix}},{k = 0},{\ldots\mspace{14mu} 3}$ 2${\frac{1}{2}\begin{bmatrix}1 & 0 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & 0 \\0 & 1 \\0 & {\exp\left( {j\; 2\;\pi\;{k/4}} \right)}\end{bmatrix}},{k = 0},{\ldots\mspace{14mu} 3}$

TABLE 2 Table 2: Example codebook of precoder matrices W having productstructure. Tx Rank Codebook per Rank 1${\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)}\end{bmatrix}},{k = 0},{\ldots\mspace{14mu} 3}$${\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\{- 1} \\{- {\exp\left( {j\; 2\;\pi\;{k/4}} \right)}}\end{bmatrix}},{k = 0},{\ldots\mspace{14mu} 3}$ 2${\frac{1}{2}\begin{bmatrix}1 & 1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & {\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\1 & {- 1} \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & {- {\exp\left( {j\; 2\;\pi\;{k/4}} \right)}}\end{bmatrix}},{k = 0},{\ldots\mspace{14mu} 3}$

The codebook in Table 2, works fine as long as the two polarizations arewell-separated, i.e., if the cross-polar discrimination (XPD) issufficiently high. To improve the performance for scenarios with mediumXPD, it is beneficial to allow the sign of the weights for the twopolarizations to vary, as exemplified by the set of matrices for {tildeover (W)} in Table 3, Table 4 and Table 5. This helps avoiding that thetwo polarizations cancel each other. The problem is then that evenmultiplying with the above V matrix leads to power imbalances among thePAs. In other words, not all elements in each precoder matrix/vectormultiplication have the same magnitude. In this case, a better choicemay be to multiply with

$V = {\begin{bmatrix}{\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} \\{\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}}\end{bmatrix}.}$

This ensures that all elements have the same amplitude and thus enablesfull use of all PAs, yet it provides the advantage of transforming +−45degree polarizations into vertical and horizontal polarizations, whichprovide better separation of the streams in multi-stream mode.

The codebooks and the above unitary matrices can easily be generalizedto other transmit array sizes (i.e., other than four antennas) and it isalso possible to multiply the precoder elements from the right with somepossibly unitary matrix or matrices and additional matrixmultiplications from the left as well. This includes permuting the rowsand/or columns of the precoder elements. These codebooks can also besubsets of larger codebooks. In conjunction to this, it should be notedthat there are many equivalent ways of expressing the above productstructure, in particular for the block diagonalizing unitary matrix V.For example, other equivalent forms of expressing the first exemplifiedV would be

$\begin{bmatrix}1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}$ ${or}\begin{bmatrix}{- 1} & 0 & 1 & 0 \\0 & {- 1} & 0 & 1 \\1 & 0 & 1 & 0 \\0 & 1 & 0 & 1\end{bmatrix}$

In general, the notion of a block diagonalizing unitary matrix isdefined to mean a unitary (unitary up to a scaling factor) matrix suchthat for a particular cross-polarized antenna setup, it creates avirtual cross-polarized antenna setup which mimics the transmission froma cross-polarized antenna setup with vertically and horizontallypolarized antennas, which at the same time ensures that together withthe block diagonal matrices in the product structure, all scalarelements of the resulting product structure precoder matrices have thesame absolute value. Thus, the block diagonalizing unitary matrixrotates the polarizations in said manner and ensures that the use of thePAs is balanced. Furthermore the notion of a 45 degree blockdiagonalizing unitary matrix is defined to mean a block diagonalizingunitary matrix that rotates the polarization directions 45 degrees.

TABLE 3 Table 3: Example structure of set of {tilde over (W)} matricessuitable especially well for two spatially separated (small distance)cross polarized antenna pairs in SU-MIMO mode. Note that for notationalsimplicity, the scaling of the matrices so as to keep the total transmitpower constant regardless of selected precoding matrix has intentionallybeen left out. Tx Rank Codebook per Rank 1 $\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\0 \\0\end{bmatrix},{k = 0},{\ldots\mspace{14mu} 3}$ $\begin{bmatrix}0 \\0 \\1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)}\end{bmatrix},{k = 0},{\ldots\mspace{14mu} 3}$ $\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)}\end{bmatrix},{k = 0},{\ldots\mspace{14mu} 3}$ $\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\{- 1} \\{- {\exp\left( {j\; 2\;\pi\;{k/4}} \right)}}\end{bmatrix},{k = 0},{\ldots\mspace{14mu} 3}$ 2 $\begin{bmatrix}1 & 0 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & 0 \\0 & 1 \\0 & {\exp\left( {j\; 2\;\pi\;{k/4}} \right)}\end{bmatrix},{k = 0},{\ldots\mspace{14mu} 3}$ $\begin{bmatrix}1 & 1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & {\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\1 & {- 1} \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & {- {\exp\left( {j\; 2\;\pi\;{k/4}} \right)}}\end{bmatrix},{k = 0},{\ldots\mspace{14mu} 3}$

TABLE 4 Table 4: Example structure of set of {tilde over (W)} matricessuitable especially well for two spatially separated (large distance)cross polarized antenna pairs in SU-MIMO mode. Note that for notationalsimplicity, the scaling of the matrices so as to keep the total transmitpower constant regardless of selected precoding matrix has intentionallybeen left out. Tx Rank Codebook per Rank 1 $\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\0 \\0\end{bmatrix},{k = 0},\ldots\mspace{14mu},3$ $\begin{bmatrix}0 \\0 \\1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)}\end{bmatrix},{k = 0},\ldots\mspace{14mu},3$ $\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/2}} \right)} \\1 \\{\exp\left( {j\; 2\;\pi\;{k^{\prime}/2}} \right)}\end{bmatrix},{k = 0},\ldots\mspace{14mu},{{1\mspace{14mu} k^{\prime}} = 0},\ldots\mspace{14mu},1$$\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/2}} \right)} \\{- 1} \\{- {\exp\left( {j\; 2\;\pi\;{k^{\prime}/2}} \right)}}\end{bmatrix},{k = 0},\ldots\mspace{14mu},{{1\mspace{14mu} k^{\prime}} = 0},\ldots\mspace{14mu},1$2 $\begin{bmatrix}1 & 0 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & 0 \\0 & 1 \\0 & {\exp\left( {j\; 2\;\pi\;{k^{\prime}/4}} \right)}\end{bmatrix},{k = 0},\ldots\mspace{14mu},{{1\mspace{14mu} k^{\prime}} = 0},\ldots\mspace{14mu},1$$\begin{bmatrix}1 & 1 \\{\exp\left( {j\; 2\;\pi\;{k/2}} \right)} & {\exp\left( {j\; 2\;\pi\;{k/2}} \right)} \\1 & {- 1} \\{\exp\left( {j\; 2\;\pi\;{k^{\prime}/2}} \right)} & {- {\exp\left( {j\; 2\;\pi\;{k^{\prime}/2}} \right)}}\end{bmatrix},{k = 0},\ldots\mspace{14mu},{{1\mspace{14mu} k^{\prime}} = 0},\ldots\mspace{14mu},1$${W_{2 \times 2} \in W} = \left\{ {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix},\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}} \right\}$ $\begin{bmatrix}W_{2 \times 2} \\0 \\0\end{bmatrix},{W_{2 \times 2} \in W}$ $\begin{bmatrix}0 \\0 \\W_{2 \times 2}\end{bmatrix},{W_{2 \times 2} \in W}$ 3${W_{2 \times 2} \in W} = \left\{ {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix},\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}} \right\}$ $\begin{bmatrix}W_{2 \times 2} & 0 \\0 & 1 \\0 & {\exp\left( {j\; 2\;\pi\;{k^{\prime}/4}} \right)}\end{bmatrix},{W_{2 \times 2} \in W},\;{k^{\prime} = 0},\ldots\mspace{14mu},3$$\begin{bmatrix}1 & 0 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & 0 \\0 & W_{2 \times 2}\end{bmatrix},{W_{2 \times 2} \in W},\;{k = 0},\ldots\mspace{14mu},3$ 4${W_{2 \times 2} \in W} = \left\{ {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix},\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}} \right\}$ $\begin{bmatrix}W_{2 \times 2} & 0 \\0 & V_{2 \times 2}\end{bmatrix},{W_{2 \times 2} \in W},{V_{2 \times 2} \in W}$

TABLE 5 Table 5: Example structure of set of {tilde over (W)} matricessuitable especially well for two spatially separated (large distance)cross polarized antenna pairs in SU-MIMO mode. Note that for notationalsimplicity, the scaling of the matrices so as to keep the total transmitpower constant regardless of selected precoding matrix has intentionallybeen left out. Tx Rank Codebook per Rank 1 $\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} \\0 \\0\end{bmatrix},{k = 0},\ldots\mspace{14mu},3$ $\begin{bmatrix}0 \\0 \\1 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)}\end{bmatrix},{k = 0},\ldots\mspace{14mu},3$ $\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/2}} \right)} \\1 \\{\exp\left( {j\; 2\;\pi\;{k^{\prime}/2}} \right)}\end{bmatrix},{k = 0},\ldots\mspace{14mu},{{1\mspace{14mu} k^{\prime}} = 0},\ldots\mspace{14mu},1$$\begin{bmatrix}1 \\{\exp\left( {j\; 2\;\pi\;{k/2}} \right)} \\{- 1} \\{- {\exp\left( {j\; 2\;\pi\;{k^{\prime}/2}} \right)}}\end{bmatrix},{k = 0},\ldots\mspace{14mu},{{1\mspace{14mu} k^{\prime}} = 0},\ldots\mspace{14mu},1$2 $\begin{bmatrix}1 & 0 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & 0 \\0 & 1 \\0 & {\exp\left( {j\; 2\;\pi\;{k^{\prime}/4}} \right)}\end{bmatrix},{k = 0},{{\ldots\mspace{14mu} 3\mspace{14mu} k^{\prime}} = 0},\ldots\mspace{14mu},3$3 ${W_{2 \times 2} \in W} = \left\{ {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix},\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}} \right\}$ $\begin{bmatrix}W_{2 \times 2} & 0 \\0 & 1 \\0 & {\exp\left( {j\; 2\;\pi\;{k^{\prime}/4}} \right)}\end{bmatrix},{W_{2 \times 2} \in W},\;{k^{\prime} = 0},\ldots\mspace{14mu},3$$\begin{bmatrix}1 & 0 \\{\exp\left( {j\; 2\;\pi\;{k/4}} \right)} & 0 \\0 & W_{2 \times 2}\end{bmatrix},{W_{2 \times 2} \in W},\;{k = 0},\ldots\mspace{14mu},3$ 4${W_{2 \times 2} \in W} = \left\{ {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix},\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}} \right\}$ $\begin{bmatrix}W_{2 \times 2} & 0 \\0 & V_{2 \times 2}\end{bmatrix},{W_{2 \times 2} \in W},{V_{2 \times 2} \in W}$

Method steps in the first node 100 for adapting a multi-antennatransmission to the second node 120 over a wireless channel 130according to some embodiments will now be described with reference to aflowchart depicted in FIG. 4. The wireless channel 130 has at leastthree inputs and at least one output. The first node 100 and the secondnode 120 are comprised in the wireless communication system 110. Themethod comprising the steps of:

-   401. The first node obtains at least one symbol stream. The symbol    stream is is intended to be transmitted to the second node 120 over    the wireless channel.-   402. This step is optional. In some embodiments the first node 100    receives channel information from the second node 120. Channel    information is in general a quantity which is statistically related    to the wireless channel. Examples of channel information includes    channel estimates, quantized channel estimates, precoder    recommendations etc. In particular, the received channel information    may comprise a precoding matrix that the second node 120 recommends    the first node 100 to use for the step of precoding. In some    embodiments wherein said channel information comprises a channel    estimate this channel estimate may be used by the first node 100 for    determining a suitable precoder matrix for the transmission.-   403. In this step the first node 100 determines a precoding matrix    having a product structure created by a block diagonal matrix being    multiplied from the left with a block diagonalizing unitary matrix.

In some embodiments the block diagonalizing unitary matrix is a 45degree block diagonalizing unitary matrix.

In some embodiments the first node 100 has received channel informationfrom the second node 120 in the optional step 402. In these embodimentsthis step of determining the precoding matrix is performed based on thechannel information received from the second node 120.

This step of determining the precoding matrix may also be performed bybasing the determination on measurements carried out in a reverse link,i.e. measurements in the first node 100 of received signals originatingfrom transmissions from the second node 120, and/or exploiting channelreciprocity properties. Channel reciprocity means that the channel, orcertain properties of the channel, is similar in the forward (from firstnode 100 to second node 120) and reverse (from second node 120 to firstnode 100) links. The measurements on a reverse link may comprise achannel estimate.

In some embodiments the first node 100 comprises a precoding codebook180 comprising precoding elements, wherein at least half of theprecoding elements in the precoding codebook 180 have said productstructure. In this case this step may be performed by selecting theprecoding matrix having a product structure from the code book 180.

The block diagonalizing unitary matrix may e.g. be equivalent to

$\begin{bmatrix}1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1}\end{bmatrix}$ ${or}\begin{bmatrix}{\exp\left( {{j\pi}/4} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- {j\pi}}/4} \right)} \\{\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- {j\pi}}/4} \right)}}\end{bmatrix}$

-   404. The first node 100 precodes the at least one symbol stream with    the determined precoding matrix.-   405. The first node 100 then transmits the precoded at least one    symbol stream over a wireless channel 130 to the second node 120. In    some embodiments the transmission of the precoded at least one    symbol stream in the first node 100 is conducted using a    multi-antenna system with a cross-polarized antenna set-up.

To perform the method steps above, the first node 100 comprises anarrangement 500 depicted in FIG. 5. As mentioned above, the first node100 and the second node 120 are comprised in the wireless communicationsystem 110. The first node arrangement is arranged to adapt amulti-antenna transmission to a second node 120 over a wireless channel.The wireless channel 130 has at least three inputs and at least oneoutput. As mentioned above, the first node 100 and the second node 120are comprised in the wireless communication system 110.

The first node arrangement 500 comprises an obtaining unit 510configured to obtain at least one symbol stream.

The first node arrangement 500 further comprises a determining unit 520configured to determine a precoding matrix having a product structurecreated by a block diagonal matrix being multiplied from the left, witha block diagonalizing unitary matrix. In some embodiments the blockdiagonalizing unitary matrix is a 45 degree block diagonalizing unitarymatrix.

The determining unit 520 may further be configured to determine theprecoding matrix by basing the determination on measurements on areverse link and/or exploiting channel reciprocity properties.

The block diagonalizing unitary matrix may be equivalent to

$\begin{bmatrix}1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1}\end{bmatrix}$ ${{or}\begin{bmatrix}{\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} \\{\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}}\end{bmatrix}}.$

The first node arrangement 500 further comprises a precoding unit 530configured to precode the at least one symbol stream with the determinedprecoding matrix.

The first node arrangement 500 further comprises a transmitting unit 540configured to transmit the precoded at least one symbol stream over awireless channel 130 to the second node 120.

In some embodiments the first node arrangement 500 comprises a precodingcodebook 180. The precoding codebook 180 may comprise precodingelements, wherein at least half of the precoding elements in theprecoding codebook 180 have said product structure. In this case thedetermining unit 520 may be configured to select the precoding matrixhaving a product structure from the precoding codebook 180.

In some embodiments the first node arrangement 500 comprises a receivingunit 550 configured to receive channel information from the second node120. In this case the determining unit 520 may be configured todetermine the precoding matrix based on the channel information receivedfrom the second node 120.

The channel information may comprise a precoding matrix that the secondnode 120 recommends the first node 100 to use for the precoding.

In some embodiments the channel information comprises a channelestimate.

The first node arrangement 500 may further comprise a multi-antennasystem with a cross-polarized antenna set-up. In this case thetransmitting unit 540 may be configured to transmit the precoded atleast one symbol stream in the first node 100 using said multi-antenna.

Method steps in the second node 100 for receiving a multi-antennatransmission from a first node 100 over a wireless channel 130 accordingto some embodiments will now be described with reference to a flowchartdepicted in FIG. 6. The wireless channel 130 has at least three inputsand at least one output. As mentioned above, the first node 100 and thesecond node 120 are comprised in a wireless communication system 110.The method comprising the step of:

-   601. This is an optional step. The second node selects a precoding    matrix to be recommended to be used by the first node 100 for    precoding a transmission.

A precoding codebook 180, 190 may be comprised in the second node 120.In that case the recommended precoding matrix may be selected out ofsaid precoding codebook 180, 190.

-   602. This is an optional step. The second node 120 conveys channel    information to the first node 100. The channel information may be    used by the first node 100 as base for determining a precoding    matrix with which a transmission corresponding to at least one    symbol stream shall be precoded.

If the optional step 601 is performed said conveyed channel informationmay be represented by the recommended precoding matrix.

-   603. The second node 100 receives a transmission corresponding to at    least one symbol stream over a wireless channel 130 conveyed from    the first node 100. The at least one symbol stream is precoded with    a precoding matrix having a product structure created by a block    diagonal matrix being multiplied from the left, with a block    diagonalizing unitary matrix. In some embodiments the block    diagonalizing unitary matrix is a 45 degree block diagonalizing    unitary matrix.

The precoding matrix may be comprised in a precoding codebook 180, 190of finite size wherein at least half of the precoding elements in theprecoding codebook have said product structure.

The block diagonalizing unitary matrix may be equivalent to

$\begin{bmatrix}1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1}\end{bmatrix}$ ${{or}\begin{bmatrix}{\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- {j\pi}}/4} \right)} \\{\exp\left( {{j\pi}/4} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}}\end{bmatrix}}.$

In some embodiments the reception of said transmission of the precodedat least one symbol stream is performed by using a multi-antenna systemwith a cross-polarized antenna setup.

To perform the method steps above, the second node 120 comprises anarrangement 700 depicted in FIG. 7. As mentioned above, the second node120 is arranged to receive a multi-antenna transmission from a firstnode 100 over a wireless channel 130. The wireless channel has at leastthree inputs and at least one output. The first node 100 and the secondnode 120 are comprised in a wireless communication system 110.

The second node arrangement 700 comprises a receiving unit 710configured to receive a transmission corresponding to at least onesymbol stream over a wireless channel 130 conveyed from the first node100. The at least one symbol stream is precoded with a precoding matrixhaving a product structure created by a block diagonal matrix beingmultiplied from the left with a block diagonalizing unitary matrix. Insome embodiments the block diagonalizing unitary matrix is a 45 degreeblock diagonalizing unitary matrix. The precoding matrix may becomprised in a precoding codebook 180, 190 of finite size wherein atleast half of the precoding elements in the precoding codebook have saidproduct structure. The precoding codebook 180, 190 may be comprised inthe first node 100 or the second node 120.

The block diagonalizing unitary matrix may e.g. be equivalent to

$\begin{bmatrix}1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1}\end{bmatrix}$ ${{or}\begin{bmatrix}{\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} \\{\exp\left( {{j\pi}/4} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}} & 0 \\0 & {\exp\left( {{j\pi}/4} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}}\end{bmatrix}}.$

In some embodiments the second node arrangement 700 further comprises aconveying unit 720 configured to convey channel information to the firstnode 100. The channel information may be used by the first node 100 asbase for determining the precoding matrix with which the received atleast one symbol stream will be precoded.

In some embodiments the channel information arranged to be conveyedcomprises a channel estimate.

The second node arrangement 700 may further comprise a selecting unit730 configured to select the precoding matrix to be recommended to beused by the first node 100 for precoding said transmission.

The channel information arranged to be conveyed by the conveying unit720 to the first node 100, may be represented by the selected andrecommended precoding matrix.

In some embodiments the precoding codebook 190 is comprised in thesecond node 120. In this case the recommended precoding matrix may beselected out of said precoding codebook 180, 190.

In some embodiments the second node arrangement 700 further comprises amulti-antenna system with a cross-polarized antenna setup. In this casethe receiving unit 710 further may be configured to receive saidtransmission of the precoded at least one symbol stream by using saidmulti-antenna system.

Some embodiments of the present method may be described as a method forenhancing performance in a wireless communication environment,comprising: modifying a pre-coding scheme by multiplying one or severalof: codebook pre-coder elements, a transmitted signal, or parts thereof,before or after possible pilots, with certain unitary matrices andextending a block diagonal codebook with non-block diagonal elements.

Non-block diagonal elements may be added to the block diagonal codebookto improve performance where cross polar discrimination is not infinite.

All the elements in said codebook may be multiplied with a unitarymatrix to transform a ±45 degree cross-polarized antenna array into avirtual vertically and horizontally polarized array.

In some embodiments the same unitary matrix is chosen so as to balancepower among the power amplifiers.

Some embodiments of the present method may be described as a wirelesscommunication device comprising a processor configured to select atransmission mode of a plurality of transmission modes from a codebook,and a memory coupled with the processor. The processor is furtherconfigured to modify a pre-coding scheme in said memory by multiplyingone or several of: codebook pre-coder elements, a transmitted signal, orparts thereof, before or after possible pilots, with certain unitarymatrices and extending a block diagonal codebook with non-block diagonalelements.

Some embodiments of the present method may be described as acomputer-readable media including instructions stored thereoncomprising: instructions for processing and modifying a pre-codingscheme by multiplying one or several of: codebook pre-coder elements, atransmitted signal, or parts thereof, before or after possible pilots,with certain unitary matrices and extending a block diagonal codebookwith non-block diagonal elements.

The present mechanism for adapting a multi-antenna transmissiontransmitted from a first node over a wireless channel and being receivedby a second node 120 may be implemented through one or more processors,such as the processor 560 in the first node arrangement 500 depicted inFIG. 5 or the processor 740 in the second node arrangement 700 depictedin FIG. 7, together with computer program code for performing thefunctions of the present solution. The program code mentioned above mayalso be provided as a computer program product, for instance in the formof a data carrier carrying computer program code for performing thepresent solution when being loaded into the first node 100 or the secondnode 120. One such carrier may be in the form of a CD ROM disc. It ishowever feasible with other data carriers such as a memory stick. Thecomputer program code can furthermore be provided as pure program codeon a server and downloaded to first node 100 or second node 120remotely.

When using the word “comprise” or “comprising” it shall be interpretedas non-limiting, i.e. meaning “consist at least of”.

The present invention is not limited to the above described embodiments.Various alternatives, modifications and equivalents may be used.Therefore, the above embodiments should not be taken as limiting thescope of the invention, which is defined by the appending claims.

1. A method in a first node for adapting a multi-antenna transmission toa second node over a wireless channel, the wireless channel having atleast three inputs and at least one output, the first node and thesecond node being included in a wireless communication system, themethod comprising the steps of: obtaining at least one symbol stream;determining a precoding matrix having a product structure created by ablock diagonal matrix being multiplied from the left with a blockdiagonalizing unitary matrix wherein the block diagonalizing unitarymatrix rotates the polarization directions of an antenna array;precoding the at least one symbol stream with the determined precodingmatrix; and transmitting the precoded at least one symbol stream over awireless channel to the second node.
 2. The method of claim 1, whereinsaid block diagonalizing unitary matrix is a 45 degree blockdiagonalizing unitary matrix configured to rotate the polarizationdirections of the antenna array by 45 degrees.
 3. The method of claim 1,wherein the step of determining a precoding matrix is performed byselecting the precoding matrix having a product structure from aprecoding codebook comprising precoding elements, wherein at least halfof the precoding elements in the precoding codebook have said productstructure.
 4. The method of claim 1, wherein the block diagonalizingunitary matrix is equivalent to $\begin{bmatrix}1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1}\end{bmatrix}.$
 5. The method of claim 1, wherein the blockdiagonalizing unitary matrix is equivalent to $\begin{bmatrix}{\exp\left( {{j\pi}/4} \right)} & 0 & {\exp\left( {{- {j\pi}}/4} \right)} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- j}\;{\pi/4}} \right)} \\{\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}}\end{bmatrix}.$
 6. The method of claim 1, further comprising the stepof: receiving channel information from the second node, and wherein thestep of determining the precoding matrix is performed based on thechannel information received from the second node.
 7. The method ofclaim 6, wherein said received channel information comprises a precodingmatrix that the second node recommends the first node to use for thestep of precoding.
 8. The method of claim 6, wherein said receivedchannel information comprises a channel estimate.
 9. The method of claim1, wherein the step of determining the precoding matrix is performed byat least one of: basing the determination on measurements on a reverselink; and basing the determination on exploiting channel reciprocityproperties.
 10. The method of claim 1, wherein the transmission of theprecoded at least one symbol stream in the first node is conducted usinga multi-antenna system with a cross-polarized antenna set-up.
 11. Amethod in a second node for receiving a multi-antenna transmission froma first node over a wireless channel, the wireless channel having atleast three inputs and at least one output, the first node and thesecond node being included in a wireless communication system, themethod comprising the step of: receiving a transmission corresponding toat least one symbol stream over a wireless channel conveyed from thefirst node, which at least one symbol stream is precoded with aprecoding matrix having a product structure created by a block diagonalmatrix being multiplied from the left with a block diagonalizing unitarymatrix wherein the block diagonalizing unitary matrix rotates thepolarization directions of an antenna array.
 12. The method of claim 11,wherein said block diagonalizing unitary matrix is a 45 degree blockdiagonalizing unitary matrix configured to rotate the polarizationdirections of the antenna array by 45 degrees.
 13. The method of claim11, wherein said precoding matrix is included in a precoding codebook offinite size wherein at least half of the precoding elements in theprecoding codebook have said product structure.
 14. The method of claim11, wherein the block diagonalizing unitary matrix is equivalent to$\begin{bmatrix}1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1}\end{bmatrix}.$
 15. The method of claim 11, wherein the blockdiagonalizing unitary matrix is equivalent to $\begin{bmatrix}{\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- {j\pi}}/4} \right)} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {\exp\left( {{- {j\pi}}/4} \right)} \\{\exp\left( {{j\pi}/4} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}} & 0 \\0 & {\exp\left( {j\;{\pi/4}} \right)} & 0 & {- {\exp\left( {{- j}\;{\pi/4}} \right)}}\end{bmatrix}.$
 16. The method of claim 11, further comprising the stepof conveying channel information to the first node, which channelinformation is used by the first node as base for determining theprecoding matrix with which the received at least one symbol stream isprecoded.
 17. The method of claim 16, further comprising the step ofselecting the precoding matrix to be recommended to be used by the firstnode for precoding said transmission, wherein said conveyed channelinformation in the step of conveying the channel information to thefirst node, is represented by the recommended precoding matrix.
 18. Themethod of claim 17, wherein the precoding codebook is included in thesecond node, and wherein the recommended precoding matrix is selectedfrom said precoding codebook.
 19. The method of claim 16, wherein saidconveyed channel information comprises a channel estimate.
 20. Themethod of claim 11, wherein the reception of said transmission of theprecoded at least one symbol stream is performed by using amulti-antenna system with a cross-polarized antenna setup.
 21. Anarrangement in a first node, for adapting a multi-antenna transmissionto a second node over a wireless channel, the wireless channel having atleast three inputs and at least one output, the first node and thesecond node being included in a wireless communication system, the firstnode arrangement comprising: an obtaining unit configured to obtain atleast one symbol stream; a determining unit configured to determine aprecoding matrix having a product structure created by a block diagonalmatrix being multiplied from the left with a block diagonalizing unitarymatrix wherein the block diagonalizinq unitary matrix rotates thepolarization directions of an antenna array; a precoding unit configuredto precode the at least one symbol stream with the determined precodingmatrix; and a transmitting unit configured to transmit the precoded atleast one symbol stream over a wireless channel to the second node. 22.An arrangement in a second node, for receiving a multi-antennatransmission from a first node over a wireless channel, the wirelesschannel having at least three inputs and at least one output, the firstnode and the second node being comprised in a wireless communicationsystem, the second node arrangement comprising a receiving unitconfigured to receive a transmission corresponding to at least onesymbol stream over a wireless channel conveyed from the first node,which at least one symbol stream is precoded with a precoding matrixhaving a product structure created by a block diagonal matrix beingmultiplied from the left with a block diagonalizing unitary matrixwherein the block diagonalizing unitary matrix rotates the polarizationdirections of an antenna array.